mlsanityData to 7 Oct 2026

Influence Diagnostics in High-dimensional M-estimation: Precise Asymptotics

arXiv 2607.09250 ↗First posted 10 Jul 2026stat.ML cs.LGcited by 0

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Abstract (arXiv)

The impact of a given training point on a statistical model can be measured through its leave-one-out influence on the model parameters, which quantifies how its removal from the training set affects the learned weights. For convex M-estimation under Gaussian design, in the high-dimensional limit nasymp d, we show that the empirical distribution of influences across training points concentrates around a deterministic measure which we sharply characterize. This characterization suggests that influential samples tend to lie on average close to the decision boundary, making contact with a standard data selection heuristic in active learning.

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References · 22

  1. 2017Understanding Black-box Predictions via Influence Functionscited by 1,714
  2. 2022Beyond neural scaling laws: beating power law scaling via data pruningcited by 519
  3. 2020Influence Functions in Deep Learning Are Fragilecited by 247
  4. 2015High-Dimensional Asymptotics of Prediction: Ridge Regression and Classificationcited by 146
  5. 2022If Influence Functions are the Answer, Then What is the Question?cited by 142
  6. 2018A modern maximum-likelihood theory for high-dimensional logistic regressioncited by 79
  7. 2013A Statistical Perspective on Algorithmic Leveragingcited by 38
  8. 2024Most Influential Subset Selection: Challenges, Promises, and Beyondcited by 31
  9. 2017Optimal Subsampling for Large Sample Logistic Regressioncited by 28
  10. 2020An Automatic Finite-Sample Robustness Metric: When Can Dropping a Little Data Make a Big Difference?cited by 27
  11. 2023Towards a statistical theory of data selection under weak supervisioncited by 25
  12. 2025Improving the Scaling Laws of Synthetic Data with Deliberate Practicecited by 17
10 more
  1. 2023High-dimensional robust regression under heavy-tailed data: Asymptotics and Universalitycited by 15
  2. 2025Why Less is More (Sometimes): A Theory of Data Curationcited by 8
  3. 2019Large deviations for the perceptron model and consequences for active learningcited by 7
  4. 2022Observable adjustments in single-index models for regularized M-estimatorscited by 5
  5. 2025Local minima of the empirical risk in high dimension: General theorems and convex examplescited by 4
  6. 2026High-Dimensional Statistics: Reflections on Progress and Open Problemscited by 3
  7. 2025Testing Most Influential Setscited by 2
  8. 2021Concentration of measure and generalized product of random vectors with an application to Hanson-Wright-like inequalitiescited by 1
  9. 2022Statistical and Computational Guarantees for Influence Diagnosticscited by 1
  10. 2026Asymptotic Theory of Iterated Empirical Risk Minimization, with Applications to Active Learningcited by 1

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